christofides代码python
时间: 2023-07-03 22:31:55 浏览: 64
以下是使用Python实现Christofides算法的代码:
```
import numpy as np
import networkx as nx
# 计算两点之间的欧式距离
def euclidean_distance(a, b):
return np.sqrt(np.sum((a - b) ** 2))
# 构建最小生成树
def minimum_spanning_tree(dist_matrix):
n = dist_matrix.shape[0]
G = nx.from_numpy_matrix(dist_matrix)
T = nx.minimum_spanning_tree(G)
return nx.to_numpy_matrix(T)
# 深度优先搜索欧拉回路
def eulerian_circuit(T):
n = T.shape[0]
G = nx.from_numpy_matrix(T)
circuit = list(nx.dfs_preorder_nodes(G, 0))
return np.array([circuit[i:i+2] for i in range(len(circuit)-1)]).astype(int)
# 缩点
def vertex_contract(circuit):
n = np.max(circuit) + 1
contracted = np.arange(n)
for u, v in circuit:
if contracted[u] != contracted[v]:
old = contracted[v]
new = contracted[u]
contracted[contracted == old] = new
return contracted
# 构建哈密顿回路
def hamiltonian_circuit(circuit, contracted):
n = np.max(contracted) + 1
G = nx.Graph()
for u, v in circuit:
u1, v1 = contracted[u], contracted[v]
G.add_edge(u1, v1, weight=euclidean_distance(np.array([u]), np.array([v])))
H = nx.DiGraph()
for i in range(n):
H.add_node(i)
for i in range(n):
for j in range(n):
if i != j:
H.add_edge(i, j, weight=nx.dijkstra_path_length(G, i, j))
path = nx.dijkstra_path(H, 0, n-1)
return np.array([path[i:i+2] for i in range(len(path)-1)]).astype(int)
# Christofides算法
def christofides(dist_matrix):
T = minimum_spanning_tree(dist_matrix)
circuit = eulerian_circuit(T)
contracted = vertex_contract(circuit)
H = hamiltonian_circuit(circuit, contracted)
return H.flatten().tolist()
```
使用时,可以将旅行商问题的节点坐标作为输入距离矩阵,例如:
```
# 节点坐标
nodes = np.array([[0, 0], [1, 2], [3, 1], [2, 3]])
# 计算距离矩阵
dist_matrix = np.zeros((4, 4))
for i in range(4):
for j in range(4):
dist_matrix[i][j] = euclidean_distance(nodes[i], nodes[j])
# 使用Christofides算法求解
path = christofides(dist_matrix)
print(path) # 输出近似最优解的路径
```
注意:该代码需要安装NetworkX库,可以通过`pip install networkx`命令进行安装。